Question

Rate constant of a first order reaction is $ 0.0693\,\,{{\min }^{-1}} $ . If we start with $ 20\,mol\,{{L}^{-1}}, $ it is reduced to $ 2.5\,mol\,{{L}^{-1}} $ in:

• A. 10 min
• B. 20 min
• C. 30 min
• D. 40 min

Answer 1

The Correct Option is C

The correct answer is C:30min
For, 1st order reaction, \(k=\frac{2.303}{t}=\log \frac{a}{(a-x)}\) 
Hence, \(t=\frac{2.303}{0.0693}\times \log \frac{20}{2.5}\)
 \(=\frac{2.303}{0.0693}\times \log \,{{(2)}^{3}}\) 
\(=\frac{2.303}{0.0693}\times 3\times 0.3010=30\min\)

Answer 2

Ans: In a chemical reaction, the first order kinetics is a process in which there is a direct relation between the rate of reaction and concentration of only one reactant. Rate of reaction depends on the first power of the concentration of that reactant. 
Mathematical equation can be written as: 
r=k[A]
In this, r is the rate of reaction 
K is the rate constant 
[A] is the concentration of reactant A. 
The rate reaction decreases exponentially with time as the concentration of the reactant decreases. The  rate of consumption will slowly decrease. One example of 1st order reaction is the decay of the radioactive material. The rate will be directly proportional to the amount of the radioactive isotopes that are present.